Strain Measures for Transfer Function Approaches to Resonant Column Testing

This paper presents strain measures to accompany a recently developed transfer function approach for resonant column testing of soils using a free-free apparatus. Although a number of past studies have proposed the use of random excitation or transfer functions in various forms, the new approach is unique in that the transfer function does not involve the current or voltage from the electromagnetic drive system. Consequently, the approach eliminates the need for many device-dependent calibrations and properties, including the torque-current calibration factor, stiffness of the torsional spring connecting the active and passive beams, and mass moments of inertia for the active platen and active beam. A brief review is given of the frequency domain transfer function approach for determining the shear modulus and damping of soil and rock, and a new theoretical formulation is presented for the associated strains in the soil specimen in terms of the measured boundary motion. It is demonstrated that higher modes can possess zero arithmetic average strains; therefore, a root-mean-square strain is proposed and derived as an alternative strain metric that will be non-zero for any frequency at which a specimen is undergoing deformation. Excellent agreement is found between experimental data and the newly derived strain measures. The concepts presented herein are valid for use with harmonic or stepped-sine testing as well as broadband random excitation, whereby strains are obtained for a range of frequencies spanning multiple modes of vibration. The approach provides a rigorous theoretical model that accurately describes the physics of the experiment over a broad frequency range spanning multiple modes. Additionally, the modulus and damping can be arbitrary functions of the frequency parameter without a loss of generality in the theoretical formulation, enabling studies of frequency-dependent modulus and damping.